11

Suppose we have

$$(A + I)^n$$

where $A$ is matrix and $I$ is an identity matrix. Does the binomial theorem apply?

I know the binomial theorem but not whether it is also applicable to matrices.

Rodrigo de Azevedo
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user3753050
  • 113

2 Answers2

11

Sure. You could prove it the same way. It works because there is no difficulty about elements commuting in the case you have chosen. But it would not work for $(A+B)^n$

almagest
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10

Think about how binomial theorem is proved. You would quickly realize that the theorem can be proved by the same way for $(A+B)^n$ if $A$ and $B$ commute.

voldemort
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  • What if matrices do not commute? In particular I have to compute the trace of $L=D-A$ to the power of $k$, like $Tr[L^k]$, but matrices do not commute. – linello Aug 30 '19 at 14:42